混合噪声即插即用：基于下确卷积保真项与多先验的算法

中文摘要 AI 辅助

即插即用（PnP）算法是一类用于逆成像的迭代方法。在优化算法中，它们将灵活的保真项（编码前向算子）与预训练的图像去噪器相结合，以处理更严重的退化，如重建图像时的模糊或下采样。本研究通过使用下确卷积作为保真项，研究混合噪声前向过程的可证明收敛的PnP方法，提供了作为两种噪声上的联合最大后验估计器的统计解释，并保留了PnP方法的贝叶斯MAP解释。独立地，我们使用Davis--Yin三算子分裂将PnP公式扩展到多个先验项。此扩展可与标准保真项或所提出的混合噪声下确卷积保真项结合使用。我们验证了这些广义PnP方法在标准Kurdyka--Lojasiewicz条件下是收敛的。在拉普拉斯-高斯和泊松-高斯噪声上的数值实验表明，单先验和多先验PnP方法具有稳定的收敛性，并在保真项不匹配时出现发散。此外，具有下确卷积保真项的PnP方法能够扩展到高达38%标准差噪声，多先验达到不同的稳定点，这些稳定点定性上保留了更多的纹理特性。

英文摘要

Plug-and-Play (PnP) algorithms are a class of iterative methods for inverse imaging. Within an optimization algorithm, they combine a flexible fidelity term, encoding the forward operator, and a pretrained image denoiser, in order to deal with more severe corruptions such as blurring or downsampling when reconstructing an image. This work studies provably convergent PnP methods for mixed-noise forward processes by using the infimal convolution as a fidelity term, providing a statistical interpretation as a joint maximum a-posteriori estimator over both noises, and preserving the Bayesian MAP interpretation of PnP methods. Independently, we extend the PnP formulation to multiple prior terms using the Davis--Yin three-operator splitting. This extension can be combined with either standard fidelities or the proposed mixed-noise infimal-convolution fidelities. We verify that these generalized PnP methods are convergent under standard Kurdyka--Lojasiewicz conditions. Numerical experiments on Laplace-Gaussian and Poisson--Gaussian noise demonstrate stable convergence of single-prior and multiple-prior PnP methods, and divergence under fidelity mismatch. Furthermore, PnP with infimal convolution fidelities are able to scale to noise up to 38% standard deviation, with multiple priors reaching different stationary points that qualitatively preserve more textural properties.

发表机构

• University of Cambridge（剑桥大学）
• University of California Los Angeles（加州大学洛杉矶分校）

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